Limit-analysis of a circular cylinder obeying the Green plasticity criterion and loaded in combined tension and torsion Nadjime Pindra 1 , Jean-Baptiste Leblond 2 ∗ , Djim´ edo Kondo 2 1 Universit´ e de Lom´ e, Facult´ e des Sciences, D´ epartement de Math´ ematiques, Lom´ e, Togo 2 Sorbonne Universit´ e, Facult´ e des Sciences (formerly Universit´ e Pierre et Marie Curie), CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, Tour 65-55, 4 place Jussieu, 75252 Paris Cedex 05, France Abstract This short paper presents the limit-analysis of a cylinder with circular basis, made of an ideal- plastic material obeying Green’s yield criterion and subjected to combined tension and torsion. The exact solution of the problem is provided in the form of a statically and plastically admissible stress field and a kinematically admissible velocity field, associated via the normality rule. The overall yield locus, that is the set of pairs [tension force, torsion torque] for which unrestrained plastic flow occurs, is expressed first in parametric form, then explicitly upon elimination of the parameter involved. The explicit expression of this yield locus also entails that of the overall flow rule via the overall normality property. The impact of these results is two-fold. First, they provide a fresh example of a solution to a limit-analysis problem exceptionally combining three generally mutually exclusive features: be non-trivial, exact and explicit. Second, they provide a way of using simple experiments of combined tension and torsion of cylinders to determine the parameter characterizing the influence of the mean stress in Green’s criterion. Keywords: Circular cylinder; combined tension and torsion; Green material; limit-analysis; para- metric yield locus; explicit yield locus 1 Introduction The problem of a circular cylinder made of some elastic-ideal-plastic von Mises material and subjected to combined tension and torsion is only slightly less popular than the corresponding one for a thin tube, and has been treated several times in classical papers and textbooks (Hill, 1950; Prager and Hodge, 1951; Gaydon, 1952; Drucker, 1967; Avitzur and Pan, 1985; Chakrabarty, 1987; de Buhan, 2007; Lubliner, 2008). ∗ Corresponding author. Preprint submitted to Meccanica 20 March 2018
Limit-analysis of a circular cylinder obeying the Green plasticity criterion and loaded in combined tension and torsion
Jun 24, 2023
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Related Documents
